Numerical: Powers, Roots & Indices MCQ — 12 Practice Questions with Answers

Explanation

Check each statement separately. For statement 1, 3^4 means 3 × 3 × 3 × 3 = 81, so it is correct. For statement 2, √144 is the number whose square is 144, and 12 × 12 = 144, so √144 = 12, not 14. Statement 3 is correct because any non-zero number raised to the power 0 is 1. Statement 4 is also correct because 5^3 = 125. Therefore, the incorrect statement is 2.

Explanation

Evaluate the four expressions one by one, using the exact meaning of each symbol. First, 3^4 means 3 × 3 × 3 × 3 = 81. Next, √625 = 25 because 25 × 25 = 625. Also, ∛216 = 6 because 6 × 6 × 6 = 216. Finally, any non-zero number raised to the power 0 equals 1, so 5^0 = 1. Thus the matching is 1-81, 2-25, 3-6 and 4-1.

Explanation

Use the index laws: when powers with the same base are multiplied, add the exponents; when they are divided, subtract the exponent of the divisor. The base remains 2 throughout, so only the exponents need to be handled. Here, (2^3 × 2^5) ÷ 2^4 = 2^(3 + 5) ÷ 2^4 = 2^8 ÷ 2^4 = 2^(8 − 4) = 2^4. Now 2^4 = 2 × 2 × 2 × 2 = 16. Therefore, the simplified value is 16.

Explanation

Use the rule a^(m/n) = (nth root of a)^m. Here 81^(3/4) means the fourth root of 81, raised to the power 3. Since 81 = 3^4, the fourth root of 81 is 3. Now cube this result: 3^3 = 3 × 3 × 3 = 27. Therefore, 81^(3/4) = 27.

Explanation

Write each surd as a multiple of √2 by taking out the largest square factor. Since 98 = 49 × 2, √98 = 7√2. Since 50 = 25 × 2, √50 = 5√2. Since 18 = 9 × 2, √18 = 3√2. Now substitute these values: √98 + √50 − √18 = 7√2 + 5√2 − 3√2. Combine the coefficients of the like surd √2: 7 + 5 − 3 = 9. Therefore, the coefficient of √2 is 9.